Do I need LSTM units everywhere in the network?
For question 1) I dont understand what you are getting at... LSTM cells will work on a contiguous block of inputs, where it sequentially uses the states from a previous time step and the new input to generate the next ones.

question 2) Please look into the LSTM atchitecture 
As you see, biases are already there, is there somewhere specific you want it, that it isnt?

question 3) Generally yes, but the normalization step can be expensive (such as softmax), so if you want to get clever, you can use negative sampling or hierarchial softmax-- but generally, you you predict a probability over all possible words given the previous text